A classification of inverse limit spaces of tent maps with periodic critical points

Lois Kailhofer¹

¹ Department of Mathematics Alverno College 3401 S 39th, Milwaukee, WI 53215, U.S.A.

Fundamenta Mathematicae, Tome 177 (2003) no. 2, pp. 95-120.

Résumé

We work within the one-parameter family of symmetric tent maps, where the slope is the parameter. Given two such tent maps $f_a$, $f_b$ with periodic critical points, we show that the inverse limit spaces $({\mathbb I}_a,f_a)$ and $({\mathbb I}_b,g_b)$ are not homeomorphic when $a \neq b$. To obtain our result, we define topological substructures of a composant, called “wrapping points” and “gaps”, and identify properties of these substructures preserved under a homeomorphism.

Détail

DOI : 10.4064/fm177-2-1

Keywords: work within one parameter family symmetric tent maps where slope parameter given tent maps periodic critical points inverse limit spaces mathbb mathbb homeomorphic neq obtain result define topological substructures composant called wrapping points gaps identify properties these substructures preserved under homeomorphism